Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Reconstructing hv-convex polyominoes from orthogonal projections
Information Processing Letters
The reconstruction of polyominoes from their orthogonal projections
Information Processing Letters
Reconstruction convex polyominoes from horizontal and vertical projections II
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Reconstruction of binary matrices under fixed size neighborhood constraints
Theoretical Computer Science
Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Note: A solvable case of image reconstruction in discrete tomography
Discrete Applied Mathematics
Reconstruction of 8-connected but not 4-connected hv-convex discrete sets
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Solving some instances of the 2-color problem
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Solving the two color problem: an heuristic algorithm
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
A reconstruction algorithm for a subclass of instances of the 2-color problem
Theoretical Computer Science
A tomographical characterization of l-convex polyominoes
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
SIAM Journal on Discrete Mathematics
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Discrete tomography deals with the reconstruction of discrete sets with given projections relative to a limited number of directions, modeling the situation where a material is studied through x-rays and we desire to reconstruct an image representing the scanned object. In many cases it would be interesting to consider the projections to be related to more than one distinguishable type of cell, called atoms or colors, as in the case of a scan involving materials of different densities, as a bone and a muscle. Unfortunately the general n-color problem with n 1 is NP-complete, but in this paper we show how several polynomial reconstruction algorithms can be defined by assuming some prior knowledge on the set to be rebuilt. In detail, we study the cases where the union of the colors form a set without switches, a convex polyomino or a convex 8-connected set. We describe some efficient reconstruction algorithms and in a case we give a sufficient condition for uniqueness.